Graph-structured data and their related algorithms have attracted significant attention in many fields, such as influenza prediction in public health. However, the variable influenza seasonality, occasional pandemics, and domain knowledge pose great challenges to construct an appropriate graph, which could impair the strength of the current popular graph-based algorithms to perform data analysis. In this study, we develop a novel method, Dynamic Virtual Graph Significance Networks (DVGSN), which can supervisedly and dynamically learn from similar "infection situations" in historical timepoints. Representation learning on the dynamic virtual graph can tackle the varied seasonality and pandemics, and therefore improve the performance. The extensive experiments on real-world influenza data demonstrate that DVGSN significantly outperforms the current state-of-the-art methods. To the best of our knowledge, this is the first attempt to supervisedly learn a dynamic virtual graph for time-series prediction tasks. Moreover, the proposed method needs less domain knowledge to build a graph in advance and has rich interpretability, which makes the method more acceptable in the fields of public health, life sciences, and so on.